Temperature optimum profile

The purpose of the reaetor design is to aequire the optimum reaetor size. However, the ideal optimum reaetor size (V/F o)opp obtained by integrating the optimum temperature profile. That is. 

Techniques for approaching optimum temperature profiles for exothermic reaction, (a) Adiabatic operation of reactors with interstage cooling, (b) Countercurrent heat exchange. (Adapted from Chemical Reaction Engineering, Second Edition, by O. Levenspiel. Copyright 1972. Reprinted by permission of John Wiley and Sons, Inc.)... 

This value is considerably less than that obtained for pure adiabatic operation (19.7 tons). The heat losses tend to partially remove thermodynamic constraints on the reaction rate and permit a closer approach to the optimum temperature profile corresponding to minimum catalyst requirements. 

P4.11.01. OPTIMUM TEMPERATURE PROFILE OF REVERSIBLE FIRST AND SECOND ORDER REACTIONS. 

There may also be an optimum temperature profile. If the temperature-dependences of the specific reaction rates ki and kj are the same (if their activation energies are equal), the reaction should be run at the highest possible temperature to minimize the batch time. This maximum temperature would be a limit imposed by some constraint maximum working temperature or pressure of the equipment, further undesirable degradation or polymierization of products or reactants at very high temperatures, etc. 

If ki is less temperature-dependent that 2, the optimum temperature profile is one that starts off at a high temperature to get the first reaction going but then drops to prevent the loss of too much B. Figure 3.10 sketches typical optimum temperature and concentration profiles. Also shown in Fig. 3.10 as the dashed line is an example of an actual temperature that could be achieved in a real reactor. The reaction mass must be heated up to 7. We will use the optimum temperature profile as the setpoint signal. 

Although an optimum temperature profile may be specified from theoretical calculations, it may not be possible to achieve in practice. The maximum temperature which can be used is usually determined by the materials of reactor construction or the durability of a catalyst. Also, steep axial temperature gradients cannot be realised unless heat transfer rates are high. If heat transfer is poor and the overall process is exothermic, temperature programming of a single reactor may be impossible the reactor becomes virtually adiabatic. In cases such as these, staged reactors (discussed elsewhere in this volume) with intercoolers may be used as a compromise. 

A comparison was made between a reactor running at the optimum temperature profile and a two-stage adiabatic reactor the amount of catalyst required was calculated to be 2.3 times higher for the adiabatic reactor. Hence much less catalyst,... 

Figure 2.45 Optimum temperature profile and corresponding conversion profile for a WGS reactor with a steam reformate fee at an inititial composition of 9% CO, 9% C02, 36% H20 and 45% H2 [80] (by courtesy of W. E. TeGrotenhuis).

Temperature profiles are established so that conversion and yield objectives are achieved while not exceeding heat transfer capacity limitations. These optimum temperature profiles depend on the chemistry. For example, if the reaction is reversible and exothermic, the temperature profile may ramp up to a high temperature to get the reactions going and then drop off with time to avoid the decrease in the chemical equilibrium constant at high temperature. If the reaction is reversible and endothermic, the temperature profile would rise to the highest possible temperature as quickly as possible because the chemical equilibrium constant increases with temperature. 

Table 9.8 shows the results of base case (case 1) optimisation with nominal values of operating parameters and those obtained by using worst-case design algorithm (case 2). The profit in Case 2 is based on weighted average of 20.5 nominal and 13.5 worst-case scenarios. Figure 9.17 shows nominal (optimum) and worst-case (optimum) temperature profile. 

The latest concepts are aimed at establishing a freely selectable (within limits) optimum temperature profile... 

The conversion and selectivity of the reaction can be decisively influenced by the design and the operation of the heat transfer circuit. The most obvious, although technically most complex solution, is to arrange different heat transfer circuits so as to achieve a stepwise approximation of an optimum temperature profile. The purposeful utilization of the temperature change of the heat transfer medium flowing through the reactor is technically simpler, and will be discussed here in connection with cocurrent or countercurrent cooling of a fixed-bed reactor with an exothermic reaction. 

The temperature control of an exothermic equilibrium reaction can constitute such a case. As illustrated in Figure 14B, the optimum temperature profile should in this case decrease with increasing conversion, i.e., along the tube length. On account of the equilibrium inhibition of the reaction, it is not possible for the reaction to run away in the front region. Countercurrent flow of the heat transfer medium is also advantageous for endothermic equilibrium reactions. Figure 21 shows... 

R. Jackson and I. Coward, Optimum Temperature Profiles in Tubular Reactors, Chem. Eng. Sci., 20, 911 (1965). 

R. Jackson and 1. Coward, Optimum Temperature Profiles in Tubular... 

In an element of catalyst dW the production rate per unit mass is FdxjdW. Hence Eq. (12-1) states that optimum performance is attained in the element when Tp is at a maximum. For the entire reactor to operate at optimum conditions the rate should have its maximum permissible value at every axial position. This concept has been used to predict optimum temperature profiles for single exothermic reversible reactions. ... 

Integration along the length of the reactor gives the optimal temperature profile and the maximum exit conversion. The optimum temperature profiles were calculated for the different reactors and the... 

Table 6.6 Performance under constrained optimum temperature profile.

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